Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods 
期刊名称Acta Mechanica Sinica
作者K. C. Nehar; B. E. Hachi; F. Cazes; M. Haboussi
摘要The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors (SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method, whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials, but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency (less time consuming and less spurious boundary effect).
关键词Bi-material interface crack;Mixed mode stress intensity factor;Displacement jump;X-FEM;Fatigue crack growth
参考文献1. Hadjesfandiari, A.R., Dargush, G.F.:Analysis of bi-material interface cracks with complex weighting functions and non-standard quadrature. Int. J. Solids Struct. 48, 1499-1512 (2011)  
2. Rice, J.R.:Elastic fracture mechanics concepts for interfacial cracks. J. Appl. Mech. 55, 98-103 (1988)  
3. Bjerken,C.,Persson,C.A.:Numericalmethodforcalculatingstress intensity factors for interface cracks in biomaterials. Eng. Fract. Mech. 68, 235-246 (2001)  
4. Hutchinson, J.W., Suo, Z.:Mixed mode cracking in layered materials. Adv. Appl. Mech. 29, 63-191 (1991)  
5. Williams, M.L.:The stresses around a fault or crack in dissimilar media. Bull. Seismol. Soc. Am. 49, 199-204 (1959)
6. Erdogan, F.:Stress distribution in bonded dissimilar materials with cracks. J. Appl. Mech. 32, 403-410 (1965)  
7. Rice, J.R., Sih, G.C.:Plane problems of cracks in dissimilar media. J. Appl. Mech. 32, 418-423 (1965)  
8. Lee, K.Y., Choi, H.J.:Boundary element analysis of stress intensity factors for bi-material interface cracks. Eng. Fract. Mech. 29, 461-472 (1988)  
9. Pant, M., Singh, I.V., Mishra, B.K.:Evaluation of mixed mode stress intensity factors for interface cracks using EFGM. Appl. Math. Model. 35, 3443-3459 (2011)  
10. Sharma, K., Bhasin, V., Singh, I.V., et al.:Simulation of bi-metallic interfacial cracks using element free galerkin method. Proced. Eng. 86, 685-692 (2014)  
11. An, X.M., Zhao, Z.Y., Zhang, H.H., et al.:Modeling bi-material interface cracks using the numerical manifold method. Eng. Anal. Bound. Elem. 37, 464-474 (2013)  
12. Chen, L., Liu, G.R., Nourbakhsh-Nia, N., et al.:Singular edgebased smoothed finite element method (ES-FEM) for bi-material interface cracks. Comput. Mech. 45, 109-125 (2010)  
13. Liu, G.R., Nguyen, T.T., Dai, K.Y., et al.:Theoretical aspects of the smoothed finite element method (SFEM). Int. J. Numer. Methods Eng. 71, 902-930 (2007)  
14. Hu, X.F., Wang, J.N., Yao, W.A.:A size independent enriched finite element for the modeling of bimaterial interface cracks. Comput. Struct. 172, 1-10 (2016)  
15. Xing, J.:SIF-based fracture criterion for interface cracks. Acta Mech. Sin. 32, 491-496 (2016)  
16. Moës, N., Dolbow, J., Belytschko, T.:A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131-150 (1999)  
17. Sukumar, N., Huang, Z.Y., Prévost, J.H., et al.:Partition of unity enrichment for bi-material interface cracks. Int. J. Numer. Methods Eng. 59, 1075-1102 (2004)  
18. Liu, X.Y., Xiao, Q.Z., Karihaloo, B.L.:XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials. Int. J. Numer. Methods Eng. 59, 1103-1118 (2004)  
19. Huynh, D.B.P., Belytschko, T.:The extended finite element method for fracture in composite materials. Int. J. Numer. Methods Eng. 77, 214-239 (2009)  
20. Bouhala, L., Shao, Q., Koutsawa, Y., et al.:An XFEM crack-tip enrichment for a crack terminating at a bimaterial interface. Eng. Fract. Mech. 102, 51-64 (2013)  
21. Akhondzadeh, S.H., Khoei, A.R., Broumand, P.:An efficient enrichment strategy for modeling stress singularities in isotropic composite materials with X-FEM technique. Eng. Fract. Mech. 169, 201-225 (2017)  
22. Khoei, A.R., Vahab, M., Haghighat, E., et al.:A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique. Int. J. Fract. 188, 79-108 (2014)  
23. Morioka, Y., Sun, C.T.:A simple method for determining stress intensity factors in bi-material interfacial cracks. In:Proceedings of the 18th Structures, Structural Dynamics, and Materials Conference (2010)
24. Cottrell, A.H.:Theoretical aspects of radiation damage and brittle fracture in steel pressure vessels. Iron Steel Inst. Spec. Rep. 69, 281-296 (1961)
25. Dodds, R.H., Read, D.T.:Experimental and analytical estimates of the J-integral for tensile panels containing short center cracks. Int. J. Fract. 28, 39-54 (1985)  
26. Pathak, H., Singh, A., Singh, I.V.V.:Fatigue crack growth simulations of bi-material interfacial cracks under thermo-elastic loading by extended finite element method. Eur. J. Comput. Mech. 22, 79104 (2013)
27. Bhattacharya, S., Singh, I.V., Mishra, B.K., et al.:Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM. Comput. Mech. 52, 799-814 (2013)  
28. Luo, X.:Elastic-plastic crack growth on plane strain bimaterial interface. Acta Mech. Sin. 8, 261-270 (1992)  
29. Aliabadi, M.H.:The Boundary Element Method. John Wiley & Sons, Hoboken (2002)
30. Wells, A.A.:Application of fracture mechanics at and beyond general yielding. Br. Weld. J. 10, 563-570 (1963)
31. Mukhopadhyay, N.K., Maiti, S.K., Kakodkar, A.:Review of SIF evaluation and modelling of singularities in BEM. Comput. Mech. 25, 358-375 (2000)  
32. Irwin, G.:Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361-364 (1957)
33. Moran, B., Shih, C.F.:Crack tip and associated domain integrals from momentum and energy balance. Eng. Fract. Mech. 27, 615-642 (1987)  
34. Lalonde, S.:Modélisation de la propagation des fissures dans les engrenages par la méthode des éléments de frontières.[Ph.D. Thesis], University of Québec-Montréal, France (2008) (in French)
35. Fedelinski, P., Aliabadi, M.H., Rooke, D.P.:A single-region time domain BEM for dynamic crack problems. Int. J. Solids Struct. 32, 3555-3571 (1995)  
36. Salgado, N.K., Aliabadi, M.H.:The boundary element analysis of cracked stiffened sheets, reinforced by adhesively bonded patches. Int. J. Numer. Methods Eng. 42, 195-217 (1998)  
37. Benmessaoud, A., Badaoui, M., Hachi, B.K., et al.:Modal stress intensity factor using extended finite element method. Appl. Mech. Mater. 232, 686-690 (2012)  
38. Chopp, D.L., Sukumar, N.:Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. Int. J. Eng. Sci. 41, 845-869 (2003)  
39. Zhuang, Z., Cheng, B.B.:Equilibrium state of mode-I subinterfacial crack growth in bi-materials. Int. J. Fract. 170, 27-36 (2011)  
40. Lee, H., Krishnaswamy, S.:Quasi-static propagation of subinterfacial cracks. Trans. ASME J. Appl. Mech. 67, 444-452 (2000)  
作者地址1 Laboratoire de développement en mécanique et matériaux(LDMM), Université de Djelfa, PB 3117, Djelfa, Algeria;
2 Laboratoire des Sciences des Procédés et des Matériaux(LSPM), UPR 3407, CNRS, Université Paris 13, Paris, France

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